A certificate system can be represented by a directed graph, called a certificate graph, where each node represents a user that has a public key and a private key and each edge (u, v) represents a certificate that is signed by the private key of u and contains the public key of v. Two types of damage can be done in a certificate graph when the private key of a node u in the graph is revealed to...

The main functional purpose of a water distribution network is to transport water from a source to several domestic and industrial units while at the same time satisfying various requirements on hydraulic response. All the water distribution networks perform two basic operations: firstly the water network needs to deliver adequate amounts of water to meet specific requirements, and secondly the...

Reliability of networks is an important issue in the field of graph and network. Computation of network vulnerability parameters is NP-complete for popular network topologies such as tree, Mesh, Cube, etc.In this paper, we will show that the tenacity and rupture degree parameters for trapezoid graphs can be computed in polynomial time.

The assessment of the stability and the vulnerability of complex networks is the important concept while studying of them. In the literature, a sort of measures have been given in order to assessment the stability of systems. And also, some graph-theoretic parameters have been formed to provide formulas which calculate the reliability of a network. In this paper, we study the vulnerability of s...

The problem of quantifying the vulnerability of graphs has received much attention nowadays, especially in the field of computer or communication networks. In a communication network, the vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a graph as modeling a network, the average lower 2-d...

In a communication network, several vulnerability measures are used to determine the resistance of the network to disruption of operation after the failure of certain stations or communication links. If the communication network is modeled as a simple, undirected, connected and unweighted graph G, then average lower independence number of a graph G can be considered as a measure of graph vulner...

In communication networks, greater degrees of stability or less vulnerability is required. The vulnerability of communication network measures the resistance of the network to the disruption of operation after the failure of certain stations or communication links. If the network begins losing communication links or processors, then there is a loss in its effectiveness. Thus, communication netw...

In communication networks, ”vulnerability” indicates the resistance of a network to disruptions in communication after a breakdown of some processors or communication links. We may use graphs to model networks, as graph theoretical parameters can be used to describe the stability and reliability of communication networks If we think of a graph as modeling a network, the average lower independen...